Feeling like you don't 'click' with your T could be due to a number of reasons: a) your two personalities do not gel; b) you are still getting to know and trust them; c) you find it incredibly difficult to trust anyone and it wouldn't matter WHO the T sitting scores from you was, you would feel the same - until you work through your trauma / issues of mistrust.
You feeling she is not genuine, I hope you talk to her about it - that way you can work out with her, 'is it me, or is it our working relationship?'
I have had a number of Ts over the years, and all have been very nice, and I have liked them - they had different skills and aspect I found helpful. But the T I have now, is the 'best' I have ever had - I am feeling a degree of trust I have never had before, ANd I am able to take risks and be more vulnerable with her - more so than anyone ever before.
Sure, it might be that she is really a lot 'better' than my past Ts; but I suspect it is as much to do with where I am at - and that I am finally getting to a place in my recovery that I am more readily able to let MY walls down and LET her do her jog.
Just something to be mindful of - but I do think the answer is for you to talk to her about it. It's probably more likely to do with transference on your part towards her, than it is necessarily that she is not genuine. (Unless she has given you very obvious examples that she is not genuine / can't be trusted - i.e., lied to you, not kept appointments, etc).
If that is the car, then talking about it with her, and working through it, you will probably find you can work more closely with her and build a better foundation of trust, than if you never said anything or stopped going to therapy.
I dont believe we have to 'like' our Ts - as long as they re good at their jobs, we can use our (apparent) dislike / mistrust / fear / love / sexual feelings towards them as a great healing tool to being able to work through past hurts and relationships where you have felt similar things ( i.e. - issues of transference - which is present in ALL our relationships, and ESPECIALLY present in the therapy rooms!).